ROM closure models are of three types:
(i) Functional, which use physical insight to construct the closure model.
(ii) Structural, which use mathematical tools.
(iii) Data-driven, which use available data.
The three types of ROM closure models are surveyed in [1]}.
In this tutorial, we take a different approach and, for clarity of presentation, focus on data-driven approaches, which have experienced a tremendous development over the last few years.
Specifically, in the next section, we present the data-driven variational multiscale ROM closure model.
